Many conventional shaving razor handle heads are configured to permit rotation of a razor cartridge about a pivot point. Some arrangements permit free rotation of the razor cartridge through a predetermined range about pins attached to the head and engaging an underside of the razor cartridge. Other types include arcuate bearings formed in the handle head, which mate with hooks on the underside of the razor cartridge. The arcuate bearings determine the range of pivoting motion of the cartridge. Some handle heads spring-load or bias the pivotally mounted razor cartridge toward a neutral position, such as at or near the midpoint of the predetermined range, allowing the cartridge to be displaced away from the neutral position in one direction, and to then move back to the neutral position using complicated spring configurations or requiring unique or specialized razor cartridges. Thus, there is a need for a simplified, inexpensive razor cartridge biasing device that can be used with a conventional razor cartridge.